The game is actually two main stories, with a few side plots.
Main Story 1: Queen Brahne goes insane and tries to conquer the world, and Princess Garnet must cope with the fact that her mother's turned evil, and fight against her. Meanwhile, Kuja manages to use Brahne to steal Garnet's connections to powerful summoned creatures (Eidolons) so that he may use them as weapons... Main Story 2: After the events of the first story, Kuja uses his newly-stolen power to ravage the world. Zidane and co. must save the world, and in the process, Zidane discovers his shared history with Kuja, and his true purpose in life. In the end, Zidane must confront and defeat his mad brother.
And then they have to fight against a Giant Space Flea From Nowhere in the last 10 minutes.
Great art! And I am quite content to see that somebody is giving some love to FFIX; it is one of the best games in the FF series, but sadly it appears that it wasn't so successful among fans since it is not so common to see many renditions about it.